0,9999999999999999999....is or not equal to one?

I've seen it argued that, since 1/3*3=1 and 0.33333333333…+0.33333333333…+0.33333333333…=0.99999999999… then 0.99999999999…=1. On the other hand, I would maintain that 0.99999999999… is in the open interval between 0 and 1, but 1 is not, therefore 0.99999999999… does not = 1